Application of a Model Based on Rough Set Theory (RST) for Estimating the Temperature of Brine from Vertical Ground Heat Exchangers (VGHE) Operated with a Heat Pump—A Case Study

Abstract

This work presents the results of a study that used a model based on rough set theory (RST) to assess the brine temperature of vertical ground heat exchangers (VGHEs) to feed heat pumps (HP). The purpose of this research was to replace costly brine temperature measurements with a more efficient approach. The object of this study was a public utility building located in Poland in a temperate continental climate. The building is equipped with a heating system using a brine–water HP installation with a total capacity of 234.4 kW, where the lower heat source consists of 52 vertical ground probes with a total length of 5200 m. The research was conducted during the heating season of 2018/2019. Based on the data, the heat energy production was determined, and the efficiency of the system was assessed. To predict the brine temperature from the lower heat source, a model based on RST was applied, which allows for the analysis of general, uncertain, and imprecise data. Weather data, such as air temperature, solar radiation intensity, degree days of the heating season, and thermal energy consumption in the building, were used for the analysis. The constructed model was tested on a test dataset. This model achieved good results with a Mean Absolute Percentage Error (MAPE) of 12.2%, a Coefficient of Variation Root Mean Square Error (CV RMSE) of 14.76%, a Mean Bias Error (MBE) of −1.3%, and an R-squared (R2) value of 0.98, indicating its usefulness in estimating brine temperature. These studies suggest that the described method can be useful in other buildings with HP systems and may contribute to improving the efficiency and safety of these systems.